The EU adopted a scheme in September to relocate 160,000 Syrian, Iraqi and Eritrean refugees from Greece and Italy but only 885 people have been moved to other member states since then.
European Migration Commissioner Dimitris Avramopoulos told a press conference that several member states have not yet offered to take a single asylum seeker.
But he said last week "we experienced the swift relocation of 287 people", the vast majority from Greece.
"We need to build on that positive experience and reach a speed of at least 6,000 people a month," Avramopoulos said during talks among EU interior ministers about efforts to tackle Europe's worst refugee crisis since the Second World War.
Avramopoulos recalled that he had written to the interior ministers of the 28-nation bloc to speed up the relocation scheme which was designed to boost solidarity with frontline states.
"If relocation does not work, then the whole system will collapse," Avramopoulos warned. But he added: "I am more than optimistic we will achieve this goal."
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European sources blame the delays in relocating people on a series of factors: governments trying to screen for potential jihadists in the wake of the Paris attacks, a lack of housing and education for asylum-seekers, and logistical problems over chartering planes.
They say some countries are setting unacceptable conditions by refusing Muslims, black people or large families, with Eastern European states the worst for discriminating on religious or racial grounds.